Question: Solve for $x$ and $y$ using elimination. ${2x+4y = 54}$ ${-x-3y = -37}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${2x+4y = 54}$ $-2x-6y = -74$ Add the top and bottom equations together. $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {2x+4y = 54}\thinspace$ to find $x$ ${2x + 4}{(10)}{= 54}$ $2x+40 = 54$ $2x+40{-40} = 54{-40}$ $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {-x-3y = -37}\thinspace$ and get the same answer for $x$ : ${-x - 3}{(10)}{= -37}$ ${x = 7}$